
HOME > Home 

Scientific Programme 
A very wide variety of processes in
science, engineering and biology involve evolutionary
PDE. Numerical simulations and predictions, particularly
for scientific purposes, demand the use of accurate
numerical methods for solving systems of time dependent
partial differential equations. This is most evident in
acoustics, when attempting to evolve weak signals for
long distances and for long times or in the simulation
of turbulent flow when attempting to capture small
structures on relatively coarse grids. In addition to
the classical requirement of conservation, of
fundamental importance is high
accuracy in both space and time for all processes
involved (e.g. advection, reaction, diffusion,
dispersion). However, as is wellknown from Godunov’s
theorem, accuracy of linear schemes greater than one
brings in the Gibbs phenomenon, producing solutions with
spurious oscillations. The real challenge is then to
construct nonlinear (nonoscillatory) schemes of high
accuracy, even for solving linear problems.
Significant advances have been made in the last three
decades on the construction of conservative, nonlinear
schemes of high order of accuracy in both space and time.
These advances were pioneered by the family of TVD (Total
Variation Diminishing) methods, by now a wellestablished
approach that produces relatively simple and practical
secondorder schemes. To go beyond secondorder, a high
degree of sophistication is required. There are at present
several approaches that, at least partially, fulfil some
of the basic requirements. Examples include the ENO method
and its variant the WENO method, the DG Finite Element
methods, the ADER approach and the Residual Distribution
method.
THEMES
OF THE CONFERENCE
Algorithm design, analysis
and applications of nonlinear schemes of accuracy greater
than two, following the finite difference, finite volume
or finite element approaches, methods for unsteady
problems, multiphase flows, plasma physics,
multiphysics applications, highorder mesh generation.



